Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x-4y &= -2 \\ -x-5y &= -7\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-5y = x-7$ Divide both sides by $-5$ to isolate $y$ $y = {-\dfrac{1}{5}x + \dfrac{7}{5}}$ Substitute this expression for $y$ in the first equation. $-8x-4({-\dfrac{1}{5}x + \dfrac{7}{5}}) = -2$ $-8x + \dfrac{4}{5}x - \dfrac{28}{5} = -2$ Simplify by combining terms, then solve for $x$ $-\dfrac{36}{5}x - \dfrac{28}{5} = -2$ $-\dfrac{36}{5}x = \dfrac{18}{5}$ $x = -\dfrac{1}{2}$ Substitute $-\dfrac{1}{2}$ for $x$ back into the top equation. $-8( -\dfrac{1}{2})-4y = -2$ $4-4y = -2$ $-4y = -6$ $y = \dfrac{3}{2}$ The solution is $\enspace x = -\dfrac{1}{2}, \enspace y = \dfrac{3}{2}$.